Divide in Scientific Notation Quick Check

Question

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Question
A rectangular park has an area of 1.36×108 ft2
. The length of the park is 1.6×104
ft. Divide the area by the length to find the width of the park.(1 point)
Responses

8.5×104
ft.
8.5 times 10 superscript 4 baseline ft.

8.5×102
ft.
8.5 times 10 squared ft.

8.5×103
ft.
8.5 times 10 cubed ft.

8.5×105
ft.

Answer 1

To find the width of the park, you can divide the area by the length:

\[ \text{Width} = \frac{\text{Area}}{\text{Length}} = \frac{1.36 \times 10^8 \text{ ft}^2}{1.6 \times 10^4 \text{ ft}} \]

Now, divide the coefficients and the powers of ten separately:

1. Coefficients: \[ \frac{1.36}{1.6} = 0.85 \]

2. Powers of ten: \[ \frac{10^8}{10^4} = 10^{8-4} = 10^4 \]

Now, combine the two results: \[ \text{Width} = 0.85 \times 10^4 \]

To express \(0.85\) in scientific notation, it can be rewritten as \(8.5 \times 10^{-1}\), so: \[ \text{Width} = 8.5 \times 10^{-1} \times 10^4 = 8.5 \times 10^{4 - 1} = 8.5 \times 10^3 \]

Thus, the width of the park is: \[ \boxed{8.5 \times 10^3 \text{ ft}} \]

So the correct answer is: 8.5×103 ft.